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 A164312 Numbers n such that k^n + (k-1)^n + ... + 3^n + 2^n + 1 is prime for some k. 1
 1, 2, 4, 8, 16, 1440 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS These terms have k-values {2, 2, 2, 2, 2, 5} respectively. When k = 2, the prime mentioned in the definition is given in A164307. - Derek Orr, Jun 06 2014 LINKS EXAMPLE 1^1 + 2^1 = 3 is prime (k = 2). 1^2 + 2^2 = 5 is prime (k = 2). 1^4 + 2^4 = 17 is prime (k = 2). 1^8 + 2^8 = 257 is prime (k = 2). 1^16 + 2^16 = 65537 is prime (k = 2). 1^1440 + 2^1440 + 3^1440 + 4^1440 + 5^1440 = 3.287049497374559048967261852*10^1006 = 3287049497374559048967261852 ... 458593539025033893379 is prime (k = 5). MATHEMATICA lst={}; Do[s=0; Do[If[PrimeQ[s+=n^x], AppendTo[lst, x]; Print[Date[], x]], {n, 4!}], {x, 7!}]; lst PROG (PARI) a(n)=for(k=1, 10^3, if(ispseudoprime(sum(i=1, k, i^n)), return(k))) n=1; while(n<5000, if(a(n), print1(n, ", ")); n++) \\ Derek Orr, Jun 06 2014 CROSSREFS Cf. A000215, A070592, A019434, A092506, A093179, A100270, A123599, A164307. Sequence in context: A046251 A281291 A346644 * A068806 A090804 A342773 Adjacent sequences:  A164309 A164310 A164311 * A164313 A164314 A164315 KEYWORD nonn,hard,more AUTHOR Vladimir Joseph Stephan Orlovsky, Aug 12 2009 EXTENSIONS Definition improved by Derek Orr, Jun 06 2014 STATUS approved

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Last modified August 14 18:13 EDT 2022. Contains 356122 sequences. (Running on oeis4.)